Agency

Both are forms of authority that exist as a result of the actions or representations of the principal. So this is a good question because the dividing line is, as you have correctly identified, not clearly distinct!

Implied authority exists as a result of the nature of the agent’s duties. In order to achieve / complete / perform those duties, it is potentially the case that the agent must enter into separate (but related) contracts – for instance to acquire the equipment necessary for the project. But note, other than assigning the task to the agent, the principal has no further involvement in the activities necessary to complete the project.

So, implied authority arises from the situation where the agent must carry out ancillary tasks in order to fulfil the principal’s directions.

And this is where apparent authority differs. Apparent authority arises where the principal actively represents (or allows to be represented) the agent as having the authority to perform activities in relation to the principal’s business. Where, for example, the principal allows the agent to drive a company vehicle with the company’s logo and wear a company uniform displaying the company’s logo, it would probably be apparent to the company’s customers that the agent has the authority of the company to enter into transactions on the company’s behalf.
And this would be so even though the agent does not have express authority.

As distinct from implied authority, apparent authority arises from the actions of the principal in actively or passively representing the agent as a person with authority

Is that better?